In the present manuscript, we have constructed an anisotropic solution for spherically symmetric space-time that satisfies Karmarkar’s condition in the context of $f(\mathcal{R},\mathcal{T})$ theory of gravity where $\mathcal{R}$ and $\mathcal{T}$ represent the Ricci scalar and the trace of Energy-momentum tensor, respectively. In order to achieve our goal, we chose a one of the gravitational potentials having regular behavior and obtained a closed form of the solution. This expression of the gravitational potential enables the embedding equation to be solved and the field equations to be integrated. The resulting current anisotropic solution is well-behaved and can be used to build realistic static fluid spheres. Our anisotropic solution represents compact structures like $VelaX-1$ and $4U1608-52$ to a very high degree of precision. It has also been presented that our stellar model is physically accepted and satisfies all the physical criteria required to meet for a stable hydrostatic equilibrium configuration.

在本手稿中，我们为球对称时空构造了一个各向异性解决方案，该解决方案在以下条件下满足Karmarkar的条件： $F（\mathcal{[R}，\mathcal{Ť}）$ 引力理论 $\mathcal{[R}$ 和 $\mathcal{Ť}$分别表示Ricci标量和能量动量张量的轨迹。为了实现我们的目标，我们选择了一种具有规则行为的引力势，并获得了封闭形式的解。重力势的这种表达使得能够求解嵌入方程，并且能够积分场方程。所得的当前各向异性解具有良好的行为，可用于构建逼真的静态流体球体。我们的各向异性解决方案代表了紧凑的结构，例如$\mathrm{伏特}Ë升\mathrm{一种}X-\mathrm{1个}$ 和 $4ü1608-52$达到很高的精度。还已经提出，我们的恒星模型在物理上被接受，并且满足满足稳定静水力平衡配置所需的所有物理标准。